A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moiré method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moiré fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moiré fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.

In phase-shifting digital holographic interferometry for measuring a displacement distribution of an object, holograms and reconstructed images have speckle noise and they provide large error in the calculation of displacement analysis. In order to decrease the effect of speckle noise, we previously proposed a new method using windowed holograms. In this paper, we propose a new averaging method of the obtained phase-difference values. Many phase-difference values at a point obtained by different windows for a hologram are averaged by considering the weight for each phase value. The weight is changed as the m-th power of the absolute amplitude of the complex amplitude of the reconstructed object. As the result, when the number n of the windowed holograms becomes larger, the standard deviation of the error becomes smaller. When the power m is 2, the error becomes the minimum. The standard deviation of the errors in the case of a flat plate with 316 nano-meter out-of-plane displacement is 88 pico-meter when n=1024 and m=2.

In this paper, a real-time shape measurement system using pixel-by-pixel calibration tables is developed. We proposed a shape measurement method using pixel-by-pixel calibration tables produced with multiple reference planes. In this method, all the relationships between the phase of the projected grating and the spatial coordinates can be obtained for each pixel. This method excludes a lens distortion and intensity errors of the projected grating in measurement results theoretically. Tabulation makes short-time measurement possible. The linearity of each pixel of a camera is also corrected using pixel-by-pixel calibration tables for linearity immediately after grabbing images.

Phase‐shifting digital holography is a new method for measuring the displacement distribution on the surface of an object. The authors previously proposed a windowed phase‐shifting digital holographic interferometry (windowed PSDHI). This method provides accurate displacement distributions by decreasing the effect of speckle patterns. In this study, the method is extended to analyse three‐dimensional displacement components in a microscope. Three object laser beams in the optical system are used. Four phase‐shifted holograms are recorded for each object laser beam. The complex amplitude of each reconstructed light at the object is calculated by the Fresnel diffraction integral of the complex amplitude of the hologram. The reconstructed distance is obtained at the point with the maximum of the standard deviation of the intensities of the object reconstructed with changing the reconstruction distance. The three phase‐difference values between before and after deformation provide the three‐dimensional displacement components. Theoretical treatment and experimental results of three‐dimensional displacement measurement using this method are shown.

In this paper, we apply phase-shifting digital holographic interferometry to simultaneous measurement for out-of-plane and in-plane displacements by employing two beam illuminations for an object. Phase-shifted holograms before and after displacements of the object using each of two beams are recorded by a CCD camera, separately. The complex amplitude at each pixel of the CCD plane is analyzed from the holograms taken with phase-shifting. The complex amplitude of he object is reconstructed from the complex amplitude distribution on the CCD plane using the Fresnel diffraction integral. Each directional phase difference distribution is obtained by calculating the phases before and after deformation for each directional beam. The phase distribution for out-of-plane displacements is obtained by calculating the sum of the two phase difference distributions. The phase distribution for in-plane displacements is obtained by calculating the difference of the two phase difference distributions. The phase values provide accurate displacement distribution information. Actually, when the object deforms in both out-of-plane and in-plane directions, it is possible to analyze the displacement distribution in each direction. The theory and an experiment are shown.